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distance on the coordinate plane

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distance on the coordinate plane

by mehrasa » Mon Sep 12, 2011 9:28 pm
Is point A closer to point(1,2)than to point(2,1)?

1. Point A lies on the line y=x
2. Point A lies on the line y=-x



i am not sure about the answer choice, but i know (2,1) and (1,2) are two points reflected based on y=x then the distance between A and each of these points are the same. then stat I is sufficient
however about stat II, I think it is insufficient because for each place of point A the answer will be different...

to me A can be a good choice... what is ur idea?
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by shankar.ashwin » Mon Sep 12, 2011 10:07 pm
Yup [A] IMO too.

could have P(x,y) where x and y are of same value but opp signs. Whenever you interchange the sign, you get contradictory answers, so using you cannot say
mehrasa wrote:Is point A closer to point(1,2)than to point(2,1)?

1. Point A lies on the line y=x
2. Point A lies on the line y=-x



i am not sure about the answer choice, but i know (2,1) and (1,2) are two points reflected based on y=x then the distance between A and each of these points are the same. then stat I is sufficient
however about stat II, I think it is insufficient because for each place of point A the answer will be different...

to me A can be a good choice... what is ur idea?
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by cans » Mon Sep 12, 2011 10:09 pm
(1,2) and (2,1) -> reflected on y=x.
a) A lies on y=x. thus equidistant. Sufficient
b) A lies on y=-x. if we take (0,0) -> equidistant,
if we take (1,-1), distance from (1,2) = 3 and distance from (2,1) = root(5) <3.
Thus farther from (1,2).
if we take (-2,2), distance from (2,1) = root(17) and distance from (1,2) = 3
root(17)>3 thus nearer to (1,2)
insufficient
IMO A
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by sl750 » Tue Sep 13, 2011 5:41 am
If you draw a graph for y=x, you will see that any point on the line is equidistant from both points (1,2) and (2,1). Sufficient

Statement 2 is not sufficient as we cannot say which point would be closer to point A on line y=-x
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